Recommendations for a modestly priced analog system

You can straddle the vintage and new worlds with something like the PTP Audio Solid 12. A very sensible re-imagined Lenco...
If the budget risestowards $10k there are several excellent modern direct drive tables. I'm in the trade and sell one ( STST from Germany ), or there is the Brinkmann, Technics etc.

Gonna put in my rec for a Well Tempered table like Amadeus GTA with a Soundsmith or Clearaudio MM cart. Once set up, a WTT is the most no-stress player in life.  With this you have budget for a preamp upgrade. 

Thanks everyone for great recommendations. So, with Cary SLP98P preamp upgrade to MC (step up), it will be $3000. Is there a Preamp plus phono stage that are better at this price or let's say up to around $4000?

With the Cary step up upgrade, they can also upgrade the caps and diodes. Ony a couple hundred more, and well worth it. My SLP-05 was just upgraded this year, and it was a pleasure to deal with them.
most preamps with only have high output moving magnet phono capability. So I have no other recommendations.
Good luck.

If you decide for an MC cartridge, I would buy Allnic Audio H-1202 phono preamp now in Agon. It won’t last long. I don’t have a direct experience with it, but Allnic phono stage is almost universally liked by all users, and its price is at your grab. I am actually tempted to buy that. For MC cartridges, you can go for a separate phono preamp and SUT, but I would bet Allnic is as good as any phono preamp + SUT at under $3000 or better.

Then, worry about selling your Cary SLP98P preamp and buying a line stage preamp that matches with your power amp. There have been many good advices so far. More may pour in, but too many causes confusion.

For turntables, research a little bit about different styles -- direct drive, belt drive, idler -- and choose one you like. I have all three kinds. If you want a used, it would be still better to buy one as a whole package, rather than buying a table, plinth, tonearm, cartridge, and headshell all separately. Also, shipping is always tricky, so look for something that is available local or within drive range. I bought a Denon DP-80 (with everything including an MC cartridge and HA-1000 head amp) from an audiophile who had kept it like new, and I was lucky.